Many systems have circuit implementations of a linear transformation, such as discrete Fourier transform (DFT) and/or an inverse discrete Fourier transform (IDFT). For example, communications systems that utilize multi-tone links often implement the IDFT during transmission of data and the DFT during receiving of the data. These transformations are useful in getting close to capacity from the communication channel.
The DFT and/or the IDFT are often implemented using digital circuits. This is illustrated in an existing communication system 100 shown in FIG. 1. A transmitter 110 includes an IDFT 112 and a digital-to-analog (D/A) converter 116. The IDFT 112 and the D/A converter 116 each may be clocked at a rate that is at least at the Nyquist rate (two times the symbol rate) using clock 114. A receiver 118 includes an analog-to-digital (A/D) converter 120 and a DFT 122. The A/D converter 120 and the DFT 122 each may be clocked at least at the Nyquist rate using clock 124. At high data rates, however, circuits, such as the transmitter 110 and the receiver 118, may have excessive sampling rates, i.e., high frequencies for the clocks 114 and 124, and resolution or quantization requirements. As a consequence, digital implementations of transformations such as the IDFT 112 and the DFT 122, may be complex, costly and may consume significant amounts of power. There is a need, therefore, for improved linear transformation circuits.
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